Note that interestingly, momentum and position in orthogonal directions do commute and don't have uncertainty. You can know both a particle position in the x d

Note that interestingly, momentum and position in orthogonal directions do commute and don't have uncertainty. You can know both a particle position in the x direction and it's momentum in the y direction with 100% certainty. Some intuitive based explanations would give you the wrong impression here. Another way of looking at it is that momentum operator is equivalent to derivation, and derivation and multiplying by x don't commute: d/dx x - x d/dx = 1. So, depending on the order in which you measured (first momentum then position, or first position then momentum) you get a different result.